Transformer Efficiency

The efficiency of a transformer is generally given by:

$$\begin{array}{rl}\eta & =\frac{P_{\text{out}}}{P_{\text{in}}}\times 100\%\\ & =\frac{P_{\text{out}}}{P_{\text{out}}+P_{\text{loss}}}\times 100\%\\ & =\frac{P_{\text{in}}-P_{\text{loss}}}{P_{\text{in}}}\times 100\%\end{array}$$

The transformer losses are composed of copper losses (in the resistances of primary and secondary windings) and the core losses. If the results of open circuit and short circuit tests are known, calculation of efficiency is very straight forward based on the above equations.

$$\begin{array}{rl}{P}_{\text{o.c.}}& =\text{no-load losses}=\text{core loss}\\ P_{\text{s.c.}}& =\text{copper loss}\end{array}$$

Since a transformer has different efficiencies at different times based on the loading level, utilities normally present efficiency in the form of all-day energy efficiency, which is defined as:

$${\eta }_e=\frac{\text{Output energy over 24 hours}}{\text{Input energy over 24 hours}}\times 100\%$$